57.2.1 problem 1

Internal problem ID [9055]
Book : First order enumerated odes
Section : section 2 (system of first order odes)
Problem number : 1
Date solved : Monday, January 27, 2025 at 05:31:41 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )-x \left (t \right )&=y \left (t \right )+t\\ \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 30

dsolve([diff(x(t),t)+diff(y(t),t)-x(t)=y(t)+t,diff(x(t),t)+diff(y(t),t)=2*x(t)+3*y(t)+exp(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= -3 t -2+c_{1} {\mathrm e}^{t} \\ y \left (t \right ) &= 2 t +1-\frac {c_{1} {\mathrm e}^{t}}{2}-\frac {{\mathrm e}^{t}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 37

DSolve[{D[x[t],t]+D[y[t],t]-x[t]==y[t]+t,D[x[t],t]+D[y[t],t]==2*x[t]+3*y[t]+Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -3 t+(1+2 c_1) e^t-2 \\ y(t)\to 2 t-(1+c_1) e^t+1 \\ \end{align*}